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On Duality and the Bi-Conjugate Gradient Algorithm

Harnett, Kristin E. (2008) On Duality and the Bi-Conjugate Gradient Algorithm. Master's Thesis, University of Pittsburgh. (Unpublished)

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It is not uncommon to encounter problems that lead to large, sparse linear systems with coefficient matrices that are invertible and sparse, but have little other structure. In such problems the solution u=A¹ƒ is typically calculated only to acurately compute functionals of the solution, L(u). This paper determines a method that converges rapidly to the functional's value. Specifially, a modified bi-conjugate gradient algorithm is found to generate convergence to the solution of linear functionals, L(u), much more rapidly than convergence to the linear system solution u.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Harnett, Kristin E.kehst42@pitt.eduKEHST42
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairLayton, Williamwjl@pitt.eduWJL
Committee MemberRebholz, Leo
Committee MemberSussman, Mike
Date: 28 September 2008
Date Type: Completion
Defense Date: 24 April 2008
Approval Date: 28 September 2008
Submission Date: 27 July 2008
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: MS - Master of Science
Thesis Type: Master's Thesis
Refereed: Yes
Uncontrolled Keywords: bi-conjugate gradient; biconjugate gradient; duality; functionals; iterative methods; sparse systems
Other ID:, etd-07272008-001302
Date Deposited: 10 Nov 2011 19:54
Last Modified: 15 Nov 2016 13:47


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